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Integrate sin(x) dx from 0 to pi

Worked through step by step. More integrals.

Answer
2\boxed{2}

Differentiating our antiderivative −cos⁡(x)-\cos(x) gives sin⁡(x)\sin(x), and evaluating the net area under one hump of the sine wave from 00 to π\pi correctly yields 22.

Problem: Evaluate the definite integral ∫0πsin⁡(x) dx\int_{0}^{\pi} \sin(x) \, dx.

Steps

  1. Find the antiderivative
    [−cos⁡(x)]0π[-\cos(x)]_{0}^{\pi}
  2. Apply the Fundamental Theorem of Calculus (upper limit)
    (−cos⁡(π))−(−cos⁡(0))(-\cos(\pi)) - (-\cos(0))
  3. Evaluate trigonometric values
    (−(−1))−(−(1))(-(-1)) - (-(1))
  4. Simplify the expression
    1+11 + 1
    22

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